There's a very good reason why the DMV is more strict. When you go the DMV, you're actually trying to acquire a new piece of identification -- a picture ID recognized by the government. The DMV has to make absolutely sure that you are who you say you are, because giving you a picture ID under an assumed name can open up all kinds of ways for you to wreak havoc -- you can buy things, plunder bank accounts, etc. The US driver's license is undoubtedly the most important piece of identification you'll ever have. If all you needed to get a picture ID was a photocopied birth certificate, trust me, identity theft would sure be a lot more common. Be glad that it's not sufficient.
On the other hand, the border crossing is not really not so critical. They can look in your car very quickly and identify that you're not carrying any contraband. They can look up the name on the birth certificate, and corroborate it with other evidence such as your vehicle registration, which was valid in the US. While it's possible that you've stolen someone's car, AND photocopied their birth certificate, AND gone to Canada and come back, it's really not very likely.
Besides, since you just got your learner's permit, I assume that you weren't driving when you crossed the border back from Canada. I assume that your parents were driving? If so, they probably have enough evidence of citizenship to pretty much just take their word that you're also a citizen.
The reason why we have several different forms of IDs in this country (birth certificate, driver's license, SS card, passport, etc.) is because even while it might be easy to fake one form of ID, it's becomes very difficult to fake ALL of them. Generally, if you lose one form of ID, you need the other two to get a replacement.
- Warren